Echo cancellation is commonly used in duplex communication systems in which transceivers simultaneously transmit and receive signals over the same frequency band or on mutually-adjacent bands. Echo cancellation is used to eliminate the echo of the near-end signal transmitted by the transceiver from the far-end signal that it receives. Typically, the echo of the near-end signal is very strong by comparison with the far-end signal. In Digital Subscriber Line (DSL) systems, for example, the far-end signal received by a modem may be attenuated by the channel by as much as 40-50 dB. Therefore, DSL modems and other high-speed data receivers may be required to suppress echo power by as much as 70-80 dB in order to achieve an acceptable signal-to-echo interference ratio at the receiver.
In general, the echo conditions to which a given modem is subject vary over time, due to temperature and voltage changes, for example. The echo canceller used in the modem should be able to adapt to such variations. As the level of integration and modem density in communication systems increase, the rate of change of echo conditions tends to increase, as well, due to adjacent modems being activated, deactivated or changing their operational mode. Therefore, it is important that the echo canceller be able to adapt quickly and accurately to changes in the echo conditions.
In a typical modem, the echo canceller (EC) comprises a transversal filter with tap spacing equal to the symbol interval. The EC processes an input from the transmitter, using the transversal filter, to generate an estimate of the echo signal, which is subtracted from the received signal. The resulting echo-canceled signal is then equalized and decoded to recover the data from the received signal. The echo-canceled signal itself is used as an error signal to adjust the tap coefficients of the EC transversal filter, typically by means of the well-known stochastic least-mean-square (LMS) algorithm. The LMS algorithm is described, for example, by Haykin, in Chapter 9 of Adaptive Filter Theory (3rd edition, Prentice Hall, 1996), which is incorporated herein by reference.
The error-canceled signal, however, typically contains high-level noise power, due mainly to the far-end signal itself, which is uncorrelated noise as far as the echo canceller is concerned, as well as to thermal noise and crosstalk. This high-level noise induces a slow adaptation rate, i.e., a long adaptation time constant τ. Specifically, the adaptation of the tap coefficients of the echo canceller transversal filter can be expressed as:Ck(n+1)=Ck(n)+μ·e(n)·x(n−k)  (1)Here Ck(n) is tap coefficient k at time n, μ is the adaptation step size, e(n) is the error signal, and x(n) is the tap input. Given σx as the root-mean-square (RMS) variance of the input signal to the echo canceller, and NEC as the length of the echo canceller transversal filter (in symbols), the adaptation time constant is given approximately by:
                              τ          ≈                      1                          μ              ·                              σ                X                2                                                    =                                            10                              SNR                /                10                                      ·                          N              EC                                2                                    (        2        )            In this equation, SNR is the adaptation signal/noise ratio (in dB), i.e., 10−SNR/10 
      10                  -        SNR            /      10        ≡                    σ        AD        2                    σ        FAR        2              .  σAD is the RMS variance of the adaptation noise in the echo-canceled signal, and σFAR is the RMS variance of the far-end signal (along with additive noise sources, such as crosstalk) in the echo-canceled signal.
It will be observed that τ increases with the required SNR and with NEC. For example, if the adaptation noise is required to be 50 dB weaker than the far-end signal (SNR=50 dB), and the echo canceller spans 200 symbols, then τ is 107 symbols long. The adaptation time becomes longer still if a polyphase echo canceller structure is used.
A number of solutions to the problem of long echo canceller adaptation time have been proposed. For example, Banerjea et al. describe a modem with enhanced echo canceller convergence in U.S. Pat. No. 6,240,128, whose disclosure is incorporated herein by reference. The modem includes two echo cancellers: a “conventional” echo canceller, which processes the transmitted signal and generates an echo cancellation signal for subtraction from the received signal before equalization; and a post-equalization echo canceller, which uses the equalized signal as an input to cancel residual echo signals that may result from drift in the echo characteristics during operation. The conventional echo canceller is “trained” during initial half-duplex operation of the modem, and its coefficients are then fixed, while the post-equalization echo canceller is allowed to continue adapting.